and Maximum of Magnetism of Nickel and Cobalt. 337 

 to be 



p.-*.- ry *'-*», 



J_ R a—x 



in which « is the mean radius of the ring, R the radius of the 

 section, n 1 the number of coils in the helix, and i the intensity 

 of the current. Now in integrating this before, I assumed that 

 jj, was a constant throughout the section of the ring : now we 

 have found that \x is a function of the magnetization, and hence 

 a function of the magnetizing-force ; but the latter varies in dif- 

 ferent parts of the section, and hence /jl must vary. But the 

 correction will be small, because the average value will be nearly 

 the same as if it were a constant. We may estimate the correction 

 in the following manner. Let //, and ^ be the values of those 

 quantities at any point in the section of the ring, ji! and $ the 

 values at the centre of the section, and ^ and »£), the observed 

 values. Then, by Taylor's theorem, 



But ^ = and §'= — , and so we have 



But in my Tables I have already calculated 



Q, 



/v 



■NtfO+i? + *••)' 



and as fi t is very nearly equal to fj, and *£) y to S$\ we have ap- 

 proximately 



which will give the value of fJ corresponding to Q' and XV- 

 Hence the correct values of the quantities will be ///, & } and 



7 72 



The quantities -J-{J- and -i~c~k can De obtained either by mea- 

 Phil. Mag, S. 4. Vol. '48. No. 319. Nov. 1874. Z 



